This whole thing is one of those fruitless arguments about a badly defined notion of "most people".

For instance the scope of the "especially chance" assertion has strange effects. Does "get born in the wrong year" include 300,000 years of human history? In that case chance has very little effect. You're overwhelming likely to grow up using stone tools, with a 1 in 3 chance of also having access to pottery.

But that would be silly and obviously wasn't the intended question. The intended question is one that's closer to home, a question that we care about. But how much closer to which home, and what exactly is the scope of the question? It can be made less about luck by filtering out the unlucky from the scope.